Multiparty computation (MPC) allows a group of servers (sometimes called players or parties) to provide inputs to an arithmetic (or Boolean) circuit and securely evaluate the circuit in the presence of an adversary who may corrupt a fixed portion of the servers. When the adversary corrupts a server, it learns all information stored on that server. The adversary can force corrupt servers to behave arbitrarily, irrespective of the protocol.
Although there are numerous published MPC protocols, few of the published protocols are proactively secure, in what would be considered a proactive MPC (PMPC). A previous work on a proactive MPC is the work of Rafail Ostrovsky and Moti Yung in “How to withstand mobile virus attacks,” In Proceedings of the Tenth Annual ACM Symposium on Principles of Distributed Computing, pages 51-59. ACM Press, 1991 (see the List of Incorporated Cited Literature References, Literature Reference No. 18), which is hereby incorporated by reference as though fully set forth herein. A limitation of that protocol is that it is not explicit, in that it does not provide the details of each step to perform and required computations and communication (i.e., the paper only provides a high level argument and description of why it is possible to construct such a protocol). The protocol of Ostrovsky and Yung (see Literature Reference No. 18) is also inefficient. The efficiency is not explicitly stated, but it is at least Ω(DCn3) (where D is the circuit depth, C is the number of gates in the circuit and n is the number of servers).
Thus, a continuing need exists for an efficient protocol for proactive security multiparty computation.